This paper by John Daugman, a faculty member at the University of Cambridge, delves into the statistical principles underlying iris recognition. The key to iris recognition lies in the failure of a test of statistical independence on the phase structure of iris patterns encoded by multi-scale quadrature wavelets. The combinatorial complexity of this phase information across different individuals spans about 249 degrees-of-freedom, generating a discrimination entropy of about 3.2 bits/mm² over the iris. This allows for real-time identification decisions with high accuracy, supporting exhaustive searches through large databases. The paper presents results from 9.1 million comparisons among several thousand eye images acquired in trials in Britain, the USA, Japan, and Korea. It discusses the localization and isolation of the iris, the encoding of iris patterns using 2D wavelet demodulation, and the statistical properties of the phase sequences. The test of statistical independence is implemented using a Boolean exclusive-OR operator, which detects disagreement between corresponding bits in two iris patterns. The distribution of Hamming distances between different irises follows a perfect binomial distribution, indicating that it is extremely improbable for two different irises to disagree in less than about a third of their phase information. The paper also explores the invariance of iris recognition to size, position, and orientation transformations, and the uniqueness of failing the test of statistical independence. It highlights the high confidence levels achievable in large database searches, even with a very forgiving degree of match (e.g., HD ≤ 0.32). The decision environment for iris recognition is analyzed, showing that the overlap between the distributions of same-iris and different-iris comparisons determines the error rates. The paper concludes with discussions on future developments, including the compression of iris phase codes and the exploration of minimum resolution requirements for iris recognition.This paper by John Daugman, a faculty member at the University of Cambridge, delves into the statistical principles underlying iris recognition. The key to iris recognition lies in the failure of a test of statistical independence on the phase structure of iris patterns encoded by multi-scale quadrature wavelets. The combinatorial complexity of this phase information across different individuals spans about 249 degrees-of-freedom, generating a discrimination entropy of about 3.2 bits/mm² over the iris. This allows for real-time identification decisions with high accuracy, supporting exhaustive searches through large databases. The paper presents results from 9.1 million comparisons among several thousand eye images acquired in trials in Britain, the USA, Japan, and Korea. It discusses the localization and isolation of the iris, the encoding of iris patterns using 2D wavelet demodulation, and the statistical properties of the phase sequences. The test of statistical independence is implemented using a Boolean exclusive-OR operator, which detects disagreement between corresponding bits in two iris patterns. The distribution of Hamming distances between different irises follows a perfect binomial distribution, indicating that it is extremely improbable for two different irises to disagree in less than about a third of their phase information. The paper also explores the invariance of iris recognition to size, position, and orientation transformations, and the uniqueness of failing the test of statistical independence. It highlights the high confidence levels achievable in large database searches, even with a very forgiving degree of match (e.g., HD ≤ 0.32). The decision environment for iris recognition is analyzed, showing that the overlap between the distributions of same-iris and different-iris comparisons determines the error rates. The paper concludes with discussions on future developments, including the compression of iris phase codes and the exploration of minimum resolution requirements for iris recognition.